Basic Math Examples

$w^{2} \cdot (14 w) + 14$

Step 1

Factor $14$ out of $w^{2} \cdot (14 w) + 14$ .

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Step 1.1

Factor $14$ out of $w^{2} \cdot (14 w)$ .

$14 (w^{2} \cdot (w)) + 14$

Step 1.2

Factor $14$ out of $14$ .

$14 (w^{2} \cdot (w)) + 14 (1)$

Step 1.3

Factor $14$ out of $14 (w^{2} \cdot (w)) + 14 (1)$ .

$14 (w^{2} \cdot (w) + 1)$

Step 2

Multiply $w^{2}$ by $w$ by adding the exponents.

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Step 2.1

Multiply $w^{2}$ by $w$ .

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Step 2.1.1

Raise $w$ to the power of $1$ .

$14 (w^{2} \cdot w^{1} + 1)$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$14 (w^{2 + 1} + 1)$

Step 2.2

Add $2$ and $1$ .

$14 (w^{3} + 1)$

Step 3

Rewrite $1$ as $1^{3}$ .

$14 (w^{3} + 1^{3})$

Step 4

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = w$ and $b = 1$ .

$14 ((w + 1) (w^{2} - w \cdot 1 + 1^{2}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Multiply $- 1$ by $1$ .

$14 ((w + 1) (w^{2} - w + 1^{2}))$

Step 5.1.2

One to any power is one.

$14 ((w + 1) (w^{2} - w + 1))$

Step 5.2

Remove unnecessary parentheses.

$14 (w + 1) (w^{2} - w + 1)$